Using the Population Attributable Fraction (PAF) to Assess MCH Population Outcomes

1. Using the Population Attributable Fraction (PAF) to Assess MCH Population Outcomes Deborah Rosenberg, PhD and Kristin Rankin, PhD Epidemiology and Biostatistics School of Public Health University of Illinois at Chicago

2. Day One: 8:30-12:00 Background and Overview Basic Formulas and Initial Computations Moving Beyond Crude PAFs: Organizing Multiple Factors into a Risk System Summary, Component and “Adjusted” PAFs

3. Background • Epidemiologists most commonly use ratio measures to estimate the magnitude of an association between a risk factor and an outcome • Impact measures, such as the Population Attributable Fraction (PAF), account for both the magnitude of association and the prevalence of risk in the population • PAFs are underused because of methodological concerns about how to appropriately account for the multifactorial nature of risk factors in the population

4. Background • In a multivariable context, the goal is to generate a PAF for each of multiple factors, taking into account relationships among the factors • Generating mutually exclusive and mutually adjusted PAFs is not straightforward given the overlapping distributions of exposure in the population; therefore methods that go beyond usual adjustment procedures are required • With appropriate methods, the PAF can be a tool for program planning and priority setting in public health since, unlike ratio measures, it permits sorting of risk factors according to their impact on an outcome

5. Historical Highlights • Levin’s PAF (1953) • “Indicated maximum proportion of disease attributable to a specific exposure” • If an exposure is completely eliminated, then the disease experience of all individuals would be the same as that of the “unexposed” P(E) = prevalence of the exposure in the population as a whole p0 = prevalence of the outcome in the population as a whole p2 = prevalence of the outcome in the unexposed

6. Historical Highlights • Miettenin (1974) • Adjusted PAF = Proportion of the disease that could be reduced by eliminating one risk factor, after controlling for others factors and accounting for effect modification • Bruzzi (1985)/Greenland and Drescher (1993) • Summary PAF = Proportion of the disease that could be reduced by simultaneously eliminating multiple risk factors from the population • Method for using regression modeling to generate PAFs • Benichou and Gail (1990) • Variance estimates for the adjusted and summary PAF based on the delta method

7. Example: Summary PAF for Three Risk Factors for a Health Outcome • Summary PAF = 0.457 • Components of a risk system: • complete crossclassification of factors

8. Apportioning the Summary PAF • The complete crossclassification of factors is not satisfactory because it fails to provide an overall estimate of impact for each risk factor. • Methodological work has been and is still being carried out to develop approaches that apportion the Summary PAF in a way that yields estimates of impact for each of a set of risk factors

9. Apportioning the Summary PAF • Eide and Gefeller (1995/1998) • Sequential PAF = Proportion of the disease that could be reduced by eliminating one risk factor from the population after some factors have already been eliminated First Sequential PAF = the “adjusted PAF” —the particular sequential PAF in which a risk factor is eliminated first before any other factors

10. Apportioning the Summary PAF • Ordering is imposed for eliminating risk factors from the population, while simultaneously controlling for all other factors in the model EXAMPLE (Sequence #1):Eliminate A, then B, then C Sequential PAF* (A) = (A|B, C) Sequential PAF (B)= (A U B|C) – (A|B, C) Sequential PAF (C)= (A U B U C) – (A U B|C) *First Sequential or “adjusted” PAF

11. Summary PAF Apportioned into Sequential PAFs for Sequence #1 • Eliminate A, then B, then C

12. Apportioning the Summary PAF • Eide and Gefeller (1995/1998) • Average PAF = Simple average of all sequential PAFs • Equal apportionment of risk over every possible sequence (removal orderings), since the order in which risk factors will be eliminated in the “real world” is an unknown • Based on the Shapley-solution in Game Theory • Method of fairly distributing the total profit gained by team members working in coalitions

13. Apportioning the Summary PAF:The Average PAF • Six Sequences for Three Risk Factors • Sequence #1: Eliminate A, then B, then C Sequence #2: Eliminate A, then C, then B Sequence #3: Eliminate B, then A, then C Sequence #4: Eliminate B, then C, then A Sequence #5: Eliminate C, then A, then B Sequence #6: Eliminate C, then B, then A There are a total of 6 sequential PAFs for each of the three risk factors. The Average PAF for each factor, then, is the simple average of all 6.

14. Summary PAF Apportioned into Average PAFs for Three Risk Factors

15. The Summary PAF: the Basis for Producing Multifactorial PAFs • The Summary PAF can be apportioned into: • component PAFs reflecting every possible combination of factors being considered • sequential PAFs reflecting pieces of one particular sequence in which risk factors might be eliminated • average PAFs reflecting estimates of the impact of eliminating multiple risk factors regardless of the order in which each is eliminated

16. PAFs from Different Study Designs • Cross-sectional: • Prevalence and measure of effect estimated from same data source • Interpretation: Proportion of prevalent cases that can be attributed to exposure • Cohort: • Prevalence and measure of effect estimated from same data source • Interpretation: Proportion of incident cases that can be attributed to exposure • Case-Control: • Prevalence of exposure among the cases must be used and the OR in place of the RR, using the rare disease assumption • Interpretation: Proportion of incident cases that can be attributed to exposure

17. Methodological Issues for the PAFin a Multivariable Context • In addition to different computational approaches, decisions about how variables will be considered may be different when focusing on the PAF as compared with focusing on the ratio measures of association • Differentiating the handling of modifiable and unmodifiable factors • Confounding and effect modification • Handling factors in a causal pathway

18. Analytic Considerations • Variable Selection • Modifiability • Unmodifiable factors are only used as potential confounders or effect modifiers; PAFs not calculated • Modifiable factors are factors that can possibly be altered with clear intervention strategies • Classification of risk factors as unmodifiable or modifiable depends on perspective and may alter results

19. Analytic Considerations • Model Building • Differential handling of unmodifiable and modifiable factors • Levels of measurement • Coding choices • Effect modification • within modifiable factors • across modifiable and unmodifiable factors • within unmodifiable factors • Selection of a final model may not be based on statistical significance of the ratio measure of effect • Stratified models • Defining the “significance” of PAFs

20. Analytic Considerations • Presentation and Interpretation • Average PAFs allow for the sorting of modifiable risk factors according to the potential impact of risk factor reduction strategies on an outcome in the population; Ratio measures only provide the magnitude of the association between a risk factor and a disease • The PAF is the proportion of an outcome that could be reduced if a risk factor is completely eliminated in the population – take care not to over-interpret findings

21. Analytic Considerations • So, why isn’t the multifactorial PAF used more commonly in the analysis of public health data? • No known standard statistical packages to complete all of the steps • Variance estimates for the average PAF are not yet available, either for random samples or for samples from complex designs • Currently, can only report 95% confidence intervals around crude, summary, and first sequential (adjusted) PAFs • While the interpretation of average PAFs is strengthened by evidence of causality, an average PAF cannot itself establish causality

22. Analytic Considerations • As always, having an explicit conceptual framework / logic model is important for multivariable analysis • Conceptualization is particularly critical when producing PAFs because decisions about variable handling and model building will determine the computational steps as well as influencing the substantive interpretation of results.

23. Laying the Groundwork: • An Example with Crude PAFs

24. Overview of Attributable Risk Measures • Measures based on Risk Differences • Attributable Risk • Attributable Fraction • Population Attributable Risk • Population Attributable Fraction (PAF)

25. Overview of Attributable Risk Measures • General Interpretation • Attributable Risk: The risk of an outcome attributed to a given risk factor among those with that factor • Attributable Fraction: The proportionof cases of an outcome attributable to a risk factor in those with the given risk factor • Pop. Attributable Risk: The risk of an outcome attributed to a given risk factor in the population as a whole • Pop. Attributable Fraction (PAF): Theproportion of cases of an outcome attributable to a risk factor in the population as a whole

26. Overview of Attributable Risk Measures • Equivalent / Alternative Terminology • Attributable Risk, Risk Difference • Attributable Fraction, Attributable Risk % Attributable Proportion, Etiologic Fraction • Pop. Attributable Risk • Pop. Attributable Fraction, Population Attributable Risk %, Etiologic Fraction, Attributable Risk

27. Overview of Attributable Risk Measures • Various Formulas For the Crude PAF

28. Example: Smoking and Low Birthweight • Crude RR = 10.00 = 1.60 • 6.25

29. Example: Smoking and Low BirthweightCrude Association • Interpretation of the RR v. the PAF • Women who smoke are at 1.6 times the risk of delivering a LBW infant compared to women who do not smoke. • 10.7% of LBW births can be attributed to smoking. If smoking were eliminated, we would expect 75 fewer LBW births and the LBW rate would be reduced from 7% to 6.25%

30. Example: Cocaine and Low BirthweightCrude Association • Crude RR = 30.00 = 4.77 • 6.29

31. Example: Cocaine and Low BirthweightCrude Association • Interpretation of the RR v. the PAF • Women who use cocaine are at 4.77 times the risk of delivering a LBW infant compared to women who do not use cocaine. • 10.2% of LBW births can be attributed to cocaine use. If cocaine use were eliminated, we would expect 71 fewer LBW births and the LBW rate would thus be reduced from 7% to 6.29%

32. Smoking and Low BirthweightCocaine and Low Birthweight • RR Compared to PAF • Notice that although the relative risk for the association between cocaine and low birthweight is much greater than that for smoking and low birthweight, the PAF for each is quite similar—10.7 for smoking and 10.2 for cocaine.

33. Moving Beyond Crude PAFs • Multivariable Approaches: • Organizing Multiple Factors • into a Risk System

34. PAFs Based on Organizing Multiple Factors into a Risk System • Summary PAF: The total PAF for many modifiable factors considered in a single risk system • Component PAF: The separate PAF for each unique combination of exposure levels in a risk system • “Adjusted” PAF: The PAF for eliminating a risk factor first from a risk system • Sequential PAF: The PAF for eliminating a risk factor in a particular order from a risk system; sets of sequential PAFs comprise possible removal sequences • Average PAF:The PAF summarizing all possible sequences for eliminating a risk factor

35. Extension of Basic Formulas for Multifactorial PAFs • = = • Rothman Bruzzi • k=Number of unique exposure categories created with a complete cross-classification of independent variables • pj=proportion of total cases that are in the “jth” unique exposure category • RRj=Relative risk for the “jth” exposure level compared with the common reference group Important: Note that in these formulas, the pjs are column percents

36. The Simple Case of 2 Binary Variables • Organization into a Risk system

37. Equivalence of the Rothman and Bruzzi Formulas

38. The simple case of 2 binary variables • Smoking and Cocaine • Crude RR = 1.60 Crude RR = 4.77

39. Smoking and Cocaine Organized into a Risk System • If smoking and cocaine use were recoded as a single “substance use” variable:

40. Components of each • combination of • risk factors in the • smoking-cocaine • risk system: • pj* rpj* RRj • *pj = column % • **rpj = row %

41. Component PAFs and Summary PAF for the Smoking-Cocaine Risk System • Using Rothman’s formula: • The Summary PAF is the • sum of component PAFs • + + • + = 0.16

42. Component PAFs and Summary PAF for the Smoking-Cocaine Risk System • Using Bruzzi’s formula: • With Bruzzi’s formula, the • Summary PAF is not built • from component PAFs

43. Limitation of Component PAFs from the Smoking-Cocaine Risk System • While the component PAFs of a risk system sum to the Summary PAF for the system as a whole, they do not provide mutually exclusive measures of the PAF for each risk factor • Here, the Summary PAF = 0.16, • but the two factors overlap: • the component PAFs still do not • disentangle smoking and cocaine • for those who do both

44. The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk Factor • The Stratified Approach: The PAF for eliminating a • risk factor after controlling for other risk factors • With the Rothman formula, data are organized into the more traditional strata set-up for adjustment: • Not assuming homogeneity, pj & RRj are stratum-specific: • Assuming homogeneity, Overall

45. The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor • The Stratified Approach • If there is multiplicative effect modification • in the RR... • As usual, it is inappropriate to average widely varying stratum-specific RRs, say 3.0 and 0.90, because a single average would misrepresent the magnitude of the association, and sometimes, as in this example, misrepresent the direction of the association as well.

46. The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor • The Stratified Approach • If there is not multiplicative effect modification • in the RR... • If there is no evidence of multiplicative effect modification and sample size permits, there is really nothing to be gained by not using stratum-specific estimates. Whichever formula is used, the result is a single “adjusted” PAF.

47. The “Adjusted” PAF: Obtaining a Single PAF for a Given Factor • Reorganizing the data to • get an adjusted PAF with • Rothman’s formula

48. The “Adjusted” PAF: The PAF for Smoking, Controlling for Cocaine Use* • RR=1.37 + • = • RR=1.36 • *Using stratum-specific estimates

49. The “Adjusted” PAF:The PAF for Cocaine Controlling for Smoking* • RR=4.33 + • = • RR=4.30 • *Using stratum-specific estimates

50. The “Adjusted” PAF: Obtaining a Single PAF for a Given Risk Factor • Using the Bruzzi formula, the “strata” are defined as each row of the risk system. In the smoking-cocaine risk system, then, there are 4 “strata”. • For the PAF for smoking, • controlling for cocaine use, • the 4 ps are the 4 column • percents and the 4 RRs are: • rp1/rp2 • rp2/rp2 • rp3/rp4 • rp4/rp4